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| HAL: tel-00651688, version 1 |
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| Université Sciences et Technologies - Bordeaux I (12/12/2011), Alain Lerat (Pr.) |
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| Contributions to the development of residual discretizations for hyperbolic conservation laws with application to shallow water flows |
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| Mario Ricchiuto 1, 2 |
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| (2011-12-12) |
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| In this work we review 12 years of developments in the field of residual based discretizations for hyperbolic problems and their application to the solution of the shallow water equations. Fundamental concepts related to the topic are recalled and he construction of second and higher order schemes for steady problems is presented. The generalization to time dependent problems by means of multi-step implicit time integration, space-time, and genuinely explicit techniques is thoroughly discussed. Finally, the issues of C-property, super consistency, and wetting/drying are analyzed in this framework showing the power of the residual based approach. |
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| 1: | BACCHUS (INRIA Bordeaux - Sud-Ouest) |
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INRIA – Université de Bordeaux – CNRS : UMR5800 |
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| 2: | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| subject | : | Mathematics/Numerical Analysis Environmental Sciences Engineering Sciences/Mechanics/Fluids mechanics Physics/Mechanics/Mechanics of the fluids |
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| Numerical analysis – hyperbolic problems – unstructured grids – finite elements – residual based schemes – high order schemes – time dependent problems – free surface flow – shallow water equations – positivity preservation – source terms – C-property – super consistency – long wave run up simulations – tsunami simulations |
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| Attached file list to this document: | |||||
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| tel-00651688, version 1 | |
| http://tel.archives-ouvertes.fr/tel-00651688 | |
| oai:tel.archives-ouvertes.fr:tel-00651688 | |
| From: Mario Ricchiuto | |
| Submitted on: Thursday, 15 December 2011 14:24:46 | |
| Updated on: Wednesday, 21 December 2011 15:20:26 | |
